5 August 1999
Physics Letters B 460 Ž1999. 227–235
Direct search for mass of neutrino and anomaly in the tritium
beta-spectrum
V.M. Lobashev, V.N. Aseev, A.I. Belesev, A.I. Berlev, E.V. Geraskin, A.A. Golubev,
O.V. Kazachenko, Yu.E. Kuznetsov, R.P. Ostroumov, L.A. Rivkis, B.E. Stern,
N.A. Titov, S.V. Zadorozhny, Yu.I. Zakharov
Institute for Nuclear Research, Academy of Sciences of Russia, 60-th October AnniÕersary Prospect 7a, 117312 Moscow, Russia
Received 23 April 1999
Editor: K. Winter
Abstract
Results of the ‘‘Troitsk n-mass’’ experiment on the search for the neutrino rest mass in the tritium beta-decay are
presented. Study of time dependence of anomalous, bump-like structure at the end of beta spectrum reported earlier gives
indication of periodic shift of the position of the bump with respect to the end-point energy with a period of 0.5 year. A new
upper limit for electron antineutrino rest mass mn - 2.5 eVrc 2 95% C.L. is derived after accounting for the bump. q 1999
Published by Elsevier Science B.V. All rights reserved.
Keywords: Tritium; Spectrum; Neutrino mass; Anomaly
1. Introduction
The direct or kinematical approach to the search
for the neutrino rest mass is based on the study of
neutrino momentum-energy balance in weak
semileptonic decays. In this case any dependence on
the leptonic or flavor quantum numbers is excluded.
Maximal sensitivity to mass effect may be attained
when neutrino energy is minimal. A such situation
usually can be obtained in three-body or multibody
decay. Total energy spectrum of visible particles in
the vicinity of maximal energy is dominated by the
neutrino phase space volume which is proportional
to pE where p is momentum and E total energy of
the neutrino. Deviation of this product from p 2
allows one to deduce the mass of neutrino. Smallness
of this product defines fast decreasing of the measured spectrum intensity by approaching the end
point energy and makes the main difficulty of the
experiment. At present the lowest limit for electron
neutrino mass was achieved by studying the shape of
tritium beta spectrum near its end point. The new
spectrometric facilities in Troitsk ŽMoscow. w1x and
in Mainz w2x allowed one to observe details of betaspectrum at about 5–15 eV below the end point.
Besides significant reduction of the neutrino mass
upper limit the experiment in Troitsk revealed the
presence of a bump-like anomalous structure Žfor
differential spectrum mode. in the spectrum in the
region of 5–15 eV below end point with integral
intensity of about 10y1 0 of total decay rate. A very
enigmatic feature of this structure turned out to be
0370-2693r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 0 - 2 6 9 3 Ž 9 9 . 0 0 7 8 1 - 9
228
V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
periodic shift of its position with time. This structure
in the condition of absence of understanding of its
nature plays a role of systematics for the search for
the neutrino mass, strongly increasing possible error.
2. The Troitsk n-mass set-up
The development of a new approach to spectroscopy of tritium started at the end of 1982 at the
Institute for Nuclear Research of the Russian
Academy of Sciences ŽTroitsk. w3x. Independently
similar ideas emerged at the Institute for Physics of
Mainz University w4x. The main feature of this approach is an integral electrostatic spectrometer with
strong inhomogeneous magnetic field providing
guiding and collimation of the electrons. The spectrometer represents a magnetic bottle with a large
ratio of field intensity in the bottleneck and in the
center. Cylinder electrode in the center of bottle acts
as an integral electrostatic analyzer. The earlier variant of such type spectrometer was proposed for
spectroscopy of electrons with energy below hundred
eV w5x. Extension of application area of the spectrometer toward a few tenth keV proved to be possible due to special tailoring of magnetic and electric
fields. The main advantage of such a spectrometer is
large improvement in energy resolution, amounting
to 3.5–4 eV ŽFW., and luminosity.
The strong guiding magnetic field in the spectrometer bottleneck permitted to couple it in a natural way with the gaseous windowless tritium source,
also with strong magnetic field, comprising the second essential part of the Troitsk set-up. Strict conservation of adiabaticity of electron movement over all
the length of the spectrometer and the source makes
possible to control both transmission function and
luminosity. Apparatus energy resolution function has
a very simple shape. For monochromatic electrons it
represents a step with practically linear slope. Width
of the slope is D E s E0 P Hm rH0 . where E0 – kinetic
energy of electron, H0 – magnetic field in the input
bottleneck and Hm – field in the center of the bottle.
The shape of the step was checked by means of
electron gun. Accuracy of this check was limited
only by monochromaticity of the gun Ž; 0.5 eV..
Gaseous tritium source has a number of advantages
in comparison with solid state source. The most
essential ones are: homogeneity, no correction for
backward scattering, weakness of interactions of tritium with other molecules, easy control for admixture, absence of charging effects. Details of the
set-up design and of the measurement procedure may
be found in w1,6,7x.
The tritium spectrum was measured by changing
the spectrometer stopping potential in steps. Direction of high voltage scanning was reversed each
cycle Ž1–2 h.. The measurements were made in the
range of the spectrometer potential from 18000 to
18770 V. Data acquisition system allowed one to
record amplitude and time of each detector pulse.
The detector is a small SiŽ Li . drifted semiconductor
counter with a thin window. The spectrometer stopping potential stability was checked by independent
measurement by 3 attenuators. Altogether, in the
period of 1994–1998 the time of measurement
amounted to about 200 days. Analysis of data was
done by fit of theoretical spectrum with variable
parameters and all the correction factors to experimental spectrum by means of the minimum x 2
procedure.
Experimental spectrum was corrected for dead
time, pile-up of the detector pulses, drift of the
source intensity, for cutting out of the part of the
detector spectrum, and for events of tritium decay
within the spectrometer. The latter display themselves as bunches of pulses 10–20 s long with
instant counting rate corresponding to probability
less than 10y4 –10y5 in comparison with regular
rate. They are produced by trapping of the decay
electrons in the magnetic field of spectrometer, which
represents a magnetic bottle. Trapped electrons in the
vacuum 10y9 torr gradually loose energy by ionization and ionization electrons are accelerated by electric field to the detector. The search for such events
was possible in the area of low counting rate from
18530 to 18770 eV. Below 18530 the average of
bunch counts for corresponding time was subtracted
from counts of each point. The statistical error for
these points were increased taking into account dispersion of bunch counts.
Theoretical spectrum was taken in classical form.
Its extension to negative Žunphysical. values of mn2
was taken as in w1x. The spectrum was convoluted
with integral energy losses spectrum of the electrons
V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
in the source, summed over the final states spectrum
and corrected for trapping effect in the source. The
latter was the reason for an intensity rise of the
spectrum toward low energy reported in w1x. The
final state spectrum of decay product ŽFSS. was
taken from the most recent theoretical calculations
w9x. Corrections for inelastic interactions of electrons
in tritium gas as well as the FSS spectrum corrections strongly correlate with mass of neutrino and
some other parameters of the spectrum. A special
system with electron gun and adiabatic magnetic
transportation of the electrons to the rear part of the
source was constructed in order to measure integral
spectrum of inelastic losses of electrons in tritium as
well as density of the source. These measurements
gave total inelastic interaction cross-section of electron with molecules of tritium in good accordance
with theoretical value 3.45 P 10y1 8 cm2 at electron
energy 18.6 keV. Spectrum of inelastic losses was
229
found to be somewhat different from usually accepted one. In particular, ratio of excitation to its
ionization parts proved to be equal to 0.51r0.49, in
disagreement with usually quoted 0.4r0.6.
Four parameters were used as a basic set of
variable parameters in x 2 fit procedure: normalization factor, end point energy, background and mn2 .
The end-point energy includes excitation energy of
the lowest levels of the decay product Ž; 1.6 eV..
The fit was made using spectrum interval with a low
energy boundary Ž E low . from 18000 eV to 18530
eV, and an upper boundary 18770 eV. Variation of
E low is very important for recognizing systematical
effects.
3. Anomalous structures in the spectrum
An example of the experimental spectrum near
the end-point is given in Fig. 1. Fitting of the data
Fig. 1. Part of experimental spectrum near the end-point. Solid line is the fitted theoretical spectrum with step function. Dotted line is
theoretical spectrum with subtracted step function. Upper right corner: spectrum of residuals for all measured part of spectrum. Residuals are
Ž Nexp y Ntheor .rs , where Nexp is the same as dotted line in previous plot, s is standard deviation in each point.
230
V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
with 4 basic variable parameters resulted in the value
of mn2 equal to y10–20 eV 2 mostly independent of
Ž Elow .. The negative values for mn2 obviously indicated that there exist some systematic effect, not
taken into account w1x. Inspection of the spectra
showed that there is a small enhancement near the
end point which resembles a small step superimposed on the regular spectrum. In differential mode
such addendum would be seen as a bump-like structure with a small width Žabout resolution of the
spectrometer.. Addition to the theoretical spectrum
of a step-like function with variable step size Ž D Nstep .
and position Ž Estep . made the theoretical and the
experimental spectra consistent over all the measured
part of it and brought the value of mn2 to about zero
thus eliminating the negative value problem Žsee Fig.
2..
Parameters of the step function turned out to vary
from run to run but resulted in average D Nstep about
6 P 10y1 1 of total decay intensity Žbesides the last
run. and E0 –Estep varying within 5–15 eV. In majority of the runs, where fit program was able to give
meaningful values for 6 parameter fit with step
function, the value of mn2 turned out to be about zero
within fit errors. An impossibility to obtain definite
minimum of x 2 in the 6-parameter fit for some run
was connected with a strong correlation of D Nstep
and mn2 when step position is too close to endpoint.
For such run the step parameters were obtained
putting mn2 s 0. Changeable positions of the step
with respect to end point energy from run to run for
the first look was evidence for some systematics.
The situation became more enigmatic when the values of E0 –Estep were plotted versus calendar time of
the corresponding run. The plot is given in Fig. 3.
It‘s very surprising feature turned out to be a possibility to describe the time dependence of the step
position by a sinusoidal curve.
The period of the fitted sinusoid proved to be
equal to 0,496 " 0,003 years, mean value of the
position 10,4 eV and sinusoid amplitude 4,35 eV. In
Fig. 4 dependence of x 2 on the value of the period
is given. In this plot the period was changed point by
point and three other parameters of sinusoid were
fitted. It is seen that half a year period is the most
probable one. The nearest minimum at the period of
0,238 year is narrow and has to be unstable by small
variation of parameters.
Fig. 2. Dependence of mn2 on E low for sum of data Run94, 96, 97Ž2., 98. Closed circles – fit without step function Ž4 parameter fit. Open
circles – fit with step function Ž6 parameter fit..
V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
231
Fig. 3. The step position dependence on the calendar time of measurements. Parameters of the fitted sinusoid are: Period 0,496 " 0,003 year,
mean value 10,4 "0,4 eV, amplitude 4,3 " 0,55 eV, phase 2,6 " 0,23 rad.
Combining data of all the years in one year plot
confirms that the variation of the step position have
biseasonal character Žsee Fig. 5.. It is worth while to
mention that the set of data given in Fig. 3 is
Fig. 4. The x 2 dependence on the period of sinusoid fitted to step position plot versus calendar time of measurement. Period value was
scanned and 3 other parameters were left variable. Solid line corresponds to all the run fit and dotted line to that with the last run ŽDecember
1998. being omitted.
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V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
Fig. 5. The plot of step positions versus time of the year. Fitted sinusoid is the same as in Fig. 3, but with the period being 0.500 year.
Horizontal bars are length of the run. Indexes of points are: year and number of the run.
somewhat different from that reported in w7x. Difference concerns mainly fit of the data of Runs 97.1
and 97.2. It was found that minimum of x 2 dependence on the position of the step is somewhat asymmetric. This leads to shift of minimum found by the
MINUIT program from center of parabolic curve
fitted to this minimum. Taking parameters of the
parabola for evaluation of minimum point increases
the error, but produces more reliable result. Such an
asymmetric structure of the x 2 multidimensional
surface is the consequence of discontinuity of derivative in the point Ž E0 –E . 2 s mn2 of the theoretical
spectrum. Approximation of the spectrum around
this point by bidimensional splines allows one to
avoid large errors but nevertheless may produce false
minimum and requires careful check of the minimum
given by MINUIT.
The plot of step size values given in Fig. 6 proved
to be more peculiar. The data obtained before the last
run ŽR98,3. roughly correlated with the first wiggle
of sinusoid given in Fig. 3. The larger step size
corresponded to the larger distance from the endpoint. The last measurement Ž98,3. however, being
relatively short, resulted in factor of 3 larger step
size and E0 –Estep somewhat below the sinusoid fit-
ted to previous data. This rise may signify that step
phenomenon, if not to consider it like some apparatus effect, may fluctuate in size with characteristic
time less than a month, at the same time the position
being close to sinusoid. This may be confronted with
the measurement of the Mainz group, where they did
not find the step effect a few weeks earlier w11x.
Unfortunately the Troitsk set-up did not run at that
time.
Of course the present set of data needs to be
sufficiently extended. In particular the absence of
measurement within the period July-December and
absence of continuous measurement during all the
year make possible to fit more complicated periodic
curve but with a half year component as a dominant
one. The latest revision of data revealed for a few
runs some asymmetry of spectra with respect to
direction of high voltage scanning. This asymmetry
is compensated by regular change of the direction,
but its origin is not yet spotted with a good confidence. Continuous control for stopping potential stability excludes explanation of this effect as a voltage
dependence on the direction of scanning. Control
measurement with an electron gun does not give
indication of this effect either. It is worth mentioning
V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
233
Fig. 6. Plot of step size versus time of the year. All the size values are reduced to the same intensity of source.
that some possible plasma-like effects in the spectrometer are not studied yet with a good thoroughness, though their role seems to be valid only for
background origin. Another possible apparatus effects as a reason for step appearance was considered
earlier in w1x.
At the moment it seems to be impossible to
propose any ‘‘customary’’ explanation of this phenomenon. The proximity of the oscillation period of
the step Žbump. to half period of Earth circulation
around the Sun and other features of the phenomenon allows one to remind an old speculation
about an effect produced by capture of the cosmological degenerated neutrino by tritium atoms with
emission of almost monochromatic electrons w10x. In
order to produce the bump intensity, corresponding
to 10y1 0 of total decay rate a neutrino cloud should
be supposed to exist with a density as high as
0,5 P 10 15nrcm3, that is 10 13 times more than generally accepted average density of relic massless neutrino.
Observation of bump below the end point of beta
spectrum corresponds to capture of neutrino with a
negative energy, that means assumption of binding
of neutrino in the cloud. In the case of binding
energy changing over the cloud, the Earth in its
movement produces the periodical modulation of
binding energy and correspondingly position of the
step. It is interesting to point out that this hypothetical binding energy assumed as V s E0 y Estep q
E Fermi where EFermi is calculated from the step size,
being plotted versus calender time provides somewhat better fit for sinusoid. It gives x 2 s 5,3 for
7 dof in comparison with minimum equal to 11,7 for
the previous fit.
The size of a neutrino cloud in this case must be
comparable with the Earth orbit and it eliminates
contradiction with average density of relic neutrino
in the Universe w8x. Of course this explanation of
step phenomenon is extremely speculative and may
be considered only for stimulation of further experiments.
Experimental data up to now do not exclude, that
the shape of the end-point region of the tritium
spectrum is more complicated than one-bump structure. Nevertheless it appears to be shown that the
center of gravity of the step-like enhancement Žbump.
is below the end-point of the tritium beta-spectrum,
and it undergoes periodical shift with respect to the
end-point.
234
V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
4. Neutrino mass upper limit
Deduction of the neutrino mass from the data in
presence of unexplained anomaly requires a special
approach. As it was mentioned earlier the procedure
adopted for this purpose consisted in addition to
theoretical spectrum of the step function with two
variable parameters supposing that such addition may
describe in the first approximation local enhancement in the beta-spectrum near to the end-point.
Distortion of beta-spectrum imitating the mn2 effect
should also be visible only near end point, otherwise
the effect relatively rapidly sinks in growing statistical errors at increasing E0 y E, but unlike the local
enhancement it appears as an addition to Žfor negative mn2 . or deficiency Žpositive mn2 . of the spectrum
intensity that is linearly increasing with E0 y E. This
difference allows one to separate both effects in fit
procedure. Of course the size and position of the step
being introduced as a free parameter, correlates with
mn2 and it increases the final error of neutrino mass
thus acting as a kind of systematic error. This increase compensates main part of the uncertainty of
substitution of a priory unknown anomaly shape by
the step-like function. A possibility to distinguish
neutrino mass effect from step strongly decreases
with proximity of step position to end-point due to
correlation of their parameters. Such correlation made
impossible to use the data of Run97Ž1. and 98Ž1. for
analysis on the neutrino mass in spite of their good
statistics.
Systematic errors, besides uncertainty caused by
step function, come mostly from the uncertainties of
parameters of the correction factors which are introduced in the spectrum before the fit. These factors
are: trapping effect, source density, uncertainty of
excitation and ionization parts of the inelastic cross
section, dead time, and influence of high exited FSS
part. Possible uncertainly of the energy resolution
function brings only negligible effect to mn2 at present accuracy level. Corresponding error may be
estimated as - 0.3 eV 2 . A remarkable property of
the total systematic error from these factors is its
reduction when Elow comes nearer to the end-point.
Opposite to it, the systematics connected with a
priory unknown step function increases when E low
comes closer to the end-point. Taking into account
that fit error of mn2 increases with increasing of E low
one may select the optimal E low , when the total
error, including both the fit and systematic error
taken in quadrature, is minimal. For the data given
below such Elow was found to be equal 18300–18400
eV. The corresponding results for mn2 are:
1994 mn2 s y2,7 " 10,1 fit " 4,9syst eV 2rc 4
Ž 1.
1996 mn2 s q0,5 " 7,1 fit " 2,5syst eV 2rc 4
Ž 2.
1997 Ž 2 . mn2 s y3,2 " 4,8 fit " 1,5syst eV 2rc 4
Ž 3.
1998
mn2 s y0,6 " 8,1 fit " 2.0 syst
eV rc
2
4
Ž 4.
The combined value in quadrature:
mn2 s y1,9 " 3,4 fit " 2,2 syst
eV 2rc 4
Ž 5.
Combined systematic error is obtained by averaging with weights of fit errors. From here one may
obtain the standard upper limit for mn w12x:
mn - 2,5 eVrc 2 ; Ž 95% C.L. .
Ž 6.
5. Conclusion
Reduction of upper limit for electron antineutrino
rest mass up to 2,5 eVrc 2 Ž95% C.L.. on the ’’Troitsk
n-mass’’ set-up using only part of the accumulated
statistics allows one to hope for further progress next
years. This limit however was obtained by accounting for the step-like Žin integral spectrum. anomaly
structure in the vicinity of the end-point energy of
tritium b-spectrum, first reported in w1x. Measurements carried out up to now revealed periodical
change of step position within 5–15 eV below endpoint with most probable period 0.5 year. At the
same time size of the step has more complicated
variations, amounting from 0.3 P 10y1 0 to 1.4 P 10y1 0
of total decay probability. It correlates roughly with
the first period of position sinusoid Žas in Fig. 4., but
exhibits a sudden rise of step magnitude with characteristic time less than a month in the last run. New
measurements of the tritium spectrum carried out last
year on the Mainz University neutrino set-up provided the data with a precision comparable with the
Troitsk set-up w11x. The Mainz group observed at
least in one run, step-like structure with position in
agreement with periodicity found in Troitsk. In two
other cases they didn‘t found any step-effect, thus
confirming its variability.
V.M. LobasheÕ et al.r Physics Letters B 460 (1999) 227–235
One of the most important tasks for next year will
be synchronous measurements in Mainz and Troitsk.
Such measurements may essentially clarify the origin
of the step phenomenon and will permit to improve
precision of the neutrino mass measurement to about
one eV scale, that is extremely important in present
state of neutrino physics. Of course more radical step
would be construction of a new facility with an order
of magnitude improvement of luminosity and energy
resolution. An example of such a facility was discussed in w7x.
Acknowledgements
This work was partially supported by the Russian
Foundation for Basic Research Žgrants 3903 and
18633a., by Program for Fundamental Nuclear
Physics and INTAS-RFBR grant 95-819. One of the
authors ŽV.M.L.. is very thankful to Alexander-vonHumboldt Foundation for a grant for Scientific Research. All the authors are very thankful to members
of the Mainz University neutrino mass group for
friendly collaboration. We are very thankful also to
235
M. Pendlebury for coordination of the INTAS project and G.K. Matushko for the help in preparation
of this article.
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